About 
Polyhedra
Over the past two years I have delved into the relationship between math and art.As a pseudo musician it has been easy for me to appreciate harmony in relation to sound, but I was perplexed with harmony in art. Harmonics dates back to Pythagoras who is credited with discovering musical and numerical harmony. According to tradition Pythagoras observed a blacksmith striking an anvil and noticed the sound it produced. He observed that the size of the hammer determined the tone it created. Harmonics may predate this however. In Genesis chapter 4 Jubal was the father of all those who play the lyre and pipe and his step brother Tubal-cain was the forger of all instruments of bronze and iron.I am obsessed with the Golden Ratio and the Fibonacci series. Unfortunately I never understood how to transition this concept into three-dimensions. In his book On Architecture, Alberti describes the creation of aesthetically pleasing rooms based on height, width, and depth. For me reading this was a moment of discovery. This moment launched my study into the world of classical thought.In the Classical world, the Seven Liberal Arts included:•Arithmetic -- Number in itself•Geometry -- Number in space•Music, Harmonics, or Tuning Theory -- Number in time•Astronomy or Cosmology -- Number in space and timeMany of my sculptures are based on icosahedral symmetry. The truncated icosahedron, that we recognize today as a soccer ball, is an Archimedean solid. The oldest known depiction of this form was by Piero della Francesca.My sculptures are fractal. Each paper design is constructed by a unit form which is multiplied and assembled to create a sphere. A sphere that can be faceted in a regular way is called a polyhedron. Polyhedrons, many sided volumes, have been explored by artists, mathematicians and philosophers over the millennia. They include: Plato, Archimedes, Euclid, Leonardo Da Vinci, Piero della Francesca, Albrecht Durer, Kepler…Paper is a material of our times; what once was highly valued is now easily discarded. In paper, ideas are quickly turned to form. Unlike artists of the past who were obsessed with creating sculptures in bronze and stone, I am interested in the fragility of paper. Paper can easily bend, twist, curve, compress and be pulled under tension. The speed and versatility of paper creates possibilities that would be difficult to achieve in another material.Like Plato’s cave, I am interested in depicting what is hidden. In this work, one paper form morphs into the other revealing an aspect of the icosahedron and truncated icosahedron in each paper sphere. This can be seen by looking through the “windows” in the sculptures to observe the interior. The exterior may be a truncated icosahedron while the interior is an icosahedron. The icosahedron is a volume based on the Golden Ratio and the Fibonacci series. The numbers 3 and 5 are part of this sequence. Observe how the numbers three and five generate forms and spaces throughout the sculpture. They also double from 3 to 6 and from 5 to 10.
